In terms of partnerships within the Barcelona team, Xavi and Iniesta might come to mind first as the best example of two players who share the ball with an incredible understanding, almost telepathic as people liek to say. They seem to know where one another are on the pitch all the time and whenever they're under pressure they can release the ball to their partner and then get the ball back when they're free again.
Yet there's another duo where the understanding is equally as impressive, that of Dani Alves and Lionel Messi. Alves and Messi love to play quick little give and goes or wall passes and they're not afraid to ping the ball at pace to one another - they're obviously confident in their partners' skill level. The Brazilian and the Argentine play like brothers on the soccer field. Take a look at the video below.
It's interesting how a defender like Alves can be such an important player for Barcelona. I don't think Messi would let Barcelona sell Alves. And while the Alves and Messi partnership is perhaps unique, in that they share a special understanding of the game, all Barcelona players have the ability to play in a similar fashion with all their teammates. It's like every player, from the last defender to the forward can play like a playmaker.